Abstract: Through transforming the access structures on eight participants to a total of 110 connected graphs on eight vertices, the paper studies the optimal information rate and the construction of perfect secret sharing schemes corresponding to these access structures are given in terms of the relationship between certain access structures and connected graphs. The exact values for the optimal information rate of the 101 access structures are computed and the relevant construction of perfect secret sharing schemes is discussed. At the same time, the upper and lower bounds for the information rate of other 9 access structures are computed and the upper bound on the information rate of connected graphs on eight vertices is proved.

Key words: secret sharing schemes, perfect secret sharing schemes, monotone access structure, complete multipartite graph, information rate

摘要： 运用某些存取结构与连通图之间的关系，将参与者人数为8的一类存取结构转化为连通图中顶点数为8的一类共110种图存取结构，进而研究了最优信息率及其所对应的完善秘密共享方案的构造。对其中101种图存取结构的最优信息率的精确值进行计算，并讨论了达到此信息率的秘密共享方案的具体构造方法；对余下9种存取结构的最优信息率的上下界进行计算，并证明了顶点数为8的信息率的上界。

关键词: 秘密共享方案, 完善的秘密共享方案, 单调的存取结构, 完全多划分图, 信息率